Papers › Computation of the Totient Summatory Function
Computation of the Totient Summatory Function
Lucas Augustus Brown
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An algorithm is devised for computing Φ(n) = ϕ(1) + ϕ(2) + ⋯+ ϕ(n) in time Θ(n^(2/3)) and space Θ(n^(1/3)). The starting point is an existing algorithm based on the Dirichlet hyperbola method and the Mertens function. The algorithm is then used to compute Φ(10¹⁹) = 30396355092701331435065976498046398788.
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